3.2 Singing of telephone wires and pine needlesJearl Walkerwww.flyingcircusofphysics.comFebruary 2011 When a strong breeze blows across telephone lines or power lines or through a pine forest, why can you hear the lines or needles sing? That sound, coming and going with the random play of a strong breeze, is one of the soothing aspects of being in a pine forest on an autumn day. Here is a video in which you can hear power lines singing in the wind when strong winds, with strong gusts, came through Cincinnati, Ohio:

When the breeze flows past a slender cylinder such as a wire or a pine needle, the airflow tends to form vortexes downstream of the cylinder. The vortexes are said to be shed by the cylinder, first on one side, then on the other side, then back to the first side, and so on. The formation of a vortex changes the air pressure, and so a train of air pressure changes moves downstream from the cylinder and sends out a sound wave, said to be an aeolian tone. You hear the air pressure changes due to the vortex shedding when you intercept some of the sound wave. The faster the air flows past the cylinder, the more frequently the changes occur, and so the frequency of the sound is higher.

The cylinder can oscillate like a guitar string at certain frequencies, said to be resonant frequencies. If the frequency of the pressure changes happens to match one of these resonant frequencies, the cylinder will oscillate at that frequency. Now the cylinder’s motion also sends out sound waves, and it may lock in (maintain) the frequency of the vortex shedding even if the speed of the airflow changes somewhat. When telephone or power lines oscillate, they are said to gallop. This can be of concern because galloping can rip out the rigs supporting a line on a pole or tower, especially if the rigs are also supporting ice that has formed on the line.

The whine from telephone wires may be the loudest and shrillest on very cold days because the cold temperatures cause the wires to contract and thus tighten between their supports. If the wires gallop, they can transfer motion to the supports, making them oscillate and thereby increasing the noise level.

Probably the most famous account of wires singing in the wind was in the popular song Wichita Lineman recorded by Glen Campbell. In this video of Campbell performing the song, listen for the line “I hear you singing in the wires.”

3.4 The harmonic kissJearl Walkerwww.flyingcircusofphysics.comFebruary 2012 When you speak or sing, you set up acoustic oscillations that resonant in your mouth-nose-throat cavity. That is a fancy wave of saying that you set up sound waves that reinforce one another as the waves reflect from the surfaces in the cavity. The lowest frequency of these standing waves is the fundamental, and the higher frequencies are the higher harmonics. The quality of the voice (or the musical beauty of the singing) is due to the combination of the fundamental and several of the higher harmonics.

Here is an unusual way of singing, where the mouth-nose-throat cavity of a second person is used to capture the sounds coming from the singer’s mouth. That second person can then amplify some of the captured harmonics by widening or narrowing his mouth, to change the shape of the resonating cavity.

As I explain in The Flying Circus of Physics book, the sound you hear from a person depends on the excitation of various formats in the vocal tract by the sound waves produced by the oscillating vocal folds. When a frequency of the vocal folds falls within the frequency range of a particular format, then sound at that format frequency is included in the person’s voice. The frequency (either the center frequency or the range of frequencies) of each format depends on two factors. One is the shape and length of the vocal tract, something you control when you shift your tongue or change the opening of your mouth. The other factor is the speed of sound in the vocal tract.

Normally, of course, air is in the vocal tract and the speed of sound has a certain value (about 340 meters per second). However, if the air is replaced with an air–helium mixture, the speed of sound is much faster (perhaps 900 meters per second). This speed increase shifts up all the format frequencies. The oscillations of the vocal folds are approximately the same as in air, but now the higher frequencies of those oscillations excite the shifted-up formats of the vocal tract. The relative strengths of the formats may also change. The result is that the voice now consists of higher frequencies and is no longer familiar.

The danger here should be obvious: You can live only if you breathe air (or rather, the oxygen in the air), but if you fill your lungs with helium, you no longer breathe air. You are then in a race against suffocation. As the oxygen level in your blood drops, can you get the helium back out and the air back in fast enough to avoid suffocating or your brain undergoing oxygen starvation? Hopefully the young man in the video was able to clear out the helium soon enough.

x3.9 Blue Man Group and acoustic resonanceJearl Walker www.flyingcircusofphysics.comOctober 2007 The following link takes you to a video of a performance by the Blue Man Group, a wildly popular group of musicians and performers in the United States. Here is a link to one of their performances. Look for the physics (other than the obvious physics in the guitars).

Ok, now for the physics. When a performer drums the side of a tube, he causes the walls to oscillate, which sends sound waves into both the external and internal air. You hear the sound (a sharp bang) of the impact as the sound waves travel through the external air to a microphone, but you also hear something more impressive --- the resonance of the tube.

Each strike against the tube wall produces sound in a range of wavelengths, but most are rather pointless inside the tube because they are wiped out by destructive interference. That is, for such a wavelength, the sound waves overlap so as to cancel one another. However, waves with certain wavelengths overlap so as to reinforce one another (undergo constructive interference), and those waves build up until their leakage through the open ends of the tube is loud enough for you to hear. When that happens, the tube is said to be in resonance and the wavelength at which this occurs is called the resonant wavelength.

Actually there are several resonant wavelengths at which leakage can be heard, but the longest of them, called the fundamental, dominates. However, you perceive frequency, not wavelength, and so I should say that the fundamental is the lowest frequency that is produced by the tube. It is responsible for the booming you hear from the tube.

The value of the fundamental frequency depends on the length of the tube: a longer tube means a lower frequency. So, when the performer extends the tube being played, you hear a noticeable shift in the frequency to a lower value.

Later on, when the two pipe sections are joined, notice that the frequency is even lower. However, when the sliding section is again used to change the length, there is almost no change in the frequency (at least I cannot hear a change). The change in length now is a smaller fraction of the total length and does not dramatically change the frequency.

Once a performer begins beating on a horizontal drumhead, another bit of curious physics occurs. A colored liquid has been poured onto the drumhead from a tube secreted in the performer’s clothing, and a bright light below the drum shines upward through the (transparent) drumhead and the colored liquid. However, we cannot see any evidence of the light beam until the drummer strikes the drumhead, sending a spray into the air. Then light can scatter from the drops to the camera for us to see. But as soon as the drops fall back to the drumhead, the scattering stops and we can no longer see any evidence of the light beam. To see a light beam, we need something in the path of the light to scatter some of the light to us. For the same reason, you cannot see a laser beam of visible light unless dust, smoke, or water drops lie in the beam.

Someone working with the Blue Man Group must have taken physics classes in school because physics abounds in many of their performances.

3.9 The hollow crest of the Parasaurolophus dinosaursJearl Walker www.flyingcircusofphysics.comAugust 2007 My reoccurring theme at this web site and in The Flying Circus of Physics book is that physics is everywhere, if only we would stop and look. And when we do bother to look, the physics can be really curious. Here is an example from the book.

Lambeosaurine dinosaurs had peculiar crests that were almost regal in appearance (check the links below here). Were the crests just for “show,” some fashion accessory among the dinosaurs? Well, we could speculate on the answer without end because the dinosaurs are long gone, but maybe physics can give us a strong clue about the use of the crests, especially on the lambeosuarine dinosaurs in the subfamily Parasaurolophus. As seen in the fossils, a crest on that type of dinosaur contained a bent hollow tube that was folded back on itself and two or three meters in total length, from one open end to the opposite open end. What possible purpose would such a double-open-ended tube have?

We see similar tubes in some wind musical instruments, and the purpose is for acoustic resonance to be set up inside the tube. Resonance is desirable because the sound can be quickly built up until it is loud enough for an audience to hear in a concert.

Sound can be produced in a tube by, say, blowing into or across an open end. Suppose sound waves with a particular wavelength are sent into the tube. The waves travel the length of the tube, partially reflect at the open end, and travel back through the length, overlapping the still oncoming waves. The waves disturb the air molecules, causing them to oscillate (very slightly) parallel to the length of the tube. The overlapping waves are said to undergo interference, which means that the air molecules at any point within the tube oscillate occurring to the net disturbance.

Well, for most wavelengths, the net disturbance is very slight. However, for certain wavelengths, said to be resonant wavelengths, the overlap produces a pattern along the tube. At some points, the net disturbance is strong, meaning that the air molecules oscillate significantly. Such strong oscillation occurs at (approximately) the two open ends and, depending on the actual wavelength value, at intermediate points along the tube. Because these are sound waves, strong oscillation means loud sound. The advantage of setting up resonance like this in a musical tube is that part of the sound leaks out of the tube (at an open end or through the wall) and can be heard by an audience. Resonance is a good thing (there, that is my physics tee-shirt statement for this month).

If you suddenly take resonance away from, say, a death-metal concert, all that is left are the gyrations and head-banging—and a crowd that will turn ugly very quickly. (Well, if they came to a death-metal concert, they probably were not in a very good mood to begin with.) You and I don’t hear wavelengths; instead we hear frequencies (that is what we consciously perceive). So, when resonance occurs inside a tube, we hear a strong resonant frequency.

So far, this is the stuff in every physics textbook, including the one I write. And, as with most textbook material, we can nod in agreement, do the homework, and then toss the stuff to the side. However, if you want to really succeed in life, you look for ways of applying the stuff you learn, instead of just tossing it. Can we apply my textbook discussion of resonance to the Parasauolophus dinosaurs?

Several researchers, including David B. Weishampel of the University of Pennsylvania, have suggested that the hollow crest on a Parasauolophus dinosaur is a resonance tube. When a dinosaur produced sound in its vocal organ, the sound waves could travel up into the tube. In the wide range of wavelengths produced by the vocal organ, some wavelengths would match a resonant wavelength of the tube and thus resonance would be set up, allowing the dinosaurs to be much louder than with just the vocal organ itself.

The Parasauolophus fossils indicate the crest on an adult had a tube length between 2.2 meters and 3.5 meters. The shortest resonant wavelength in a tube with two open ends is always twice the tube length. So, the shortest resonant wavelength in a crest tube was between 4.4 meters and 7.0 meters. That corresponds to a resonant frequency of between 77 hertz and 49 hertz, which is at the low frequency limit of your hearing range. The lowest frequency of a tube is called the fundamental. Higher frequencies (higher harmonics) that are integer multiples of the fundamental can also be produced if the vocal organ provides sound at the corresponding wavelengths.

The advantage of a low-frequency sound to a dinosaur is the same as to a lion roaring in a jungle or an elephant bellowing across a plain: In both environments, low-frequency sounds generally travel farther than higher frequency sounds, and thus individual dinosaurs could locate each other even when they could not see each other. Just imagine walking through a Jurassic Park type of cloned-dinosaur refuge and hearing a Parasauolophus sound off. Such a low frequency rumble would surely send shivers down your spine. Although dinosaurs are long gone, by applying some basic physics we can give a voice to their fossils.

3.9 Hearing a dinosaurJearl Walkerwww.flyingcircusofphysics.comMay 2014 In spite of stories such as Jurassic Park, we are unlikely to ever clone a dinosaur from ancient DNA, so we will never see a dinosaur. But can we possibly recreate the sounds of the dinosaurs, so that we can hear them? Well, yes. For one of the dinosaurs, that was recently done.

The crest on a Parasaurolophus dinosaur skull contained a nasal passage in the shape of a long, bent tube open at both ends.

This dinosaur apparently used its vocal organ to resonant that nasal passage at several of its harmonic frequencies, much like we vocalize by resonating our throat-mouth-nose cavity. Such vocalizations probably allowed the dinosaurs to communicate with each other, such as to warn each other of danger. If the dinosaurs were in a forest, the low frequencies (long wavelengths) of their vocalizations would have travelled farther through the maze of trees than higher frequencies (short wavelengths). Thus, the dinosaur might have adapted to its environment by evolving longer nasal passages.

In recent years computed tomography was used on several Parasaurolophus fossils to map the nasal passage. From the computations, the researchers constructed a replica of the dinosaur’s nasal passage. When they excited the replica by injected noise, the sound that was emitted mimicked the sound that an actual Parasaurolophus made long ago.

The replica is essentially a folded tube that is open at both ends. When a broad range of noise frequencies is sent into the tube, certain frequencies can set up standing waves of sound. Other frequencies result in nothing interesting, but those certain frequencies (said to be the harmonic frequencies of the tube) can result in loud sound waves leaking from the tube. The lowest such frequency is called either the first harmonic or the fundamental and is given by f = v/2L, where v is the speed of sound in air (about 343 meters per second) and L is the tube length in meters. For a tube length of 3.50 meters (about what is found in one of the fossils), the first harmonic is 49 hertz, near the low end of human hearing at about 15 hertz. The second harmonic is twice the first harmonic, the third is three times the first harmonic, and so on. When sound from the vocal organ entered a nasal passage, several of the harmonics would be produced.

Fossil skulls that contain shorter nasal passages are thought to be those of the female Parasaurolophus, which would vocalize at somewhat higher frequencies. These calculations are made assuming the nasal passages to be simple tubes. Actually, they had lots of nooks and crannies, which would vary from dinosaur to dinosaur. That variation probably made the sound from each dinosaur unique, much like the variations among human voices make each person unique.

In this next video you can hear the sound produced by the nasal-passage replica. Listen to the sound track from 23 seconds to 45 seconds. (Before and after that time interval, you hear music and not dinosaurs.)

Imagine being in a forest when a chorus of such low-frequency sounds surrounds you. The Parasaurolophus dinosaurs were big, with a length of 10 meters. The rumbling, low-frequency chorus would be bone-chilling, especially if you caught sight of the animals. Maybe our inability to clone these animals is not a bad thing after all.

3.19 Acoustic shadowsJearl Walkerwww.flyingcircusofphysics.comSeptember 2013 In the U.S. Civil War of 1862 through 1865, field commanders on both the Union and the Confederate sides depended heavily on sound to determine when battles began and where they were located. On several occasions, a commander would split his troops to attack the enemy from two directions, but the only way of coordinating the assaults was when the noise from one group’s attack signaled the other group to attack. Because the two groups may have been within a few kilometers of each other, this plan seemed reasonable and yet it sometimes failed in decisive battles.

A similar strange effect was noticed in June 1862 by the Confederate Secretary of War and one of his staff as they observed the battle of Gaines’s Mill from a hilltop at a distance of no more than two kilometers. The battle down in the valley involved at least 50 000 men and 100 pieces of field artillery, and it created a horrible amount of noise and must have been deafening to the fighting troops. Yet the two observers heard nothing of the battle during their two-hour observation. How could such a battle be inaudible only a few kilometers away? Here is a video concerning the noise or lack of noise at some of the Civil War battle sites:

There are three primary reasons why these tremendously loud battles could not be heard even a few kilometers away. (1) An intervening dense forest could have muffled the sounds by absorbing the sound waves. (2) The sound waves emitted at ground level could have been sent along paths that curved upward instead of paths tending to be horizontal. (3) The path taken by a sound wave could have been curved if either air temperature or wind speed changed with height.

Regarding the third reason, if the air temperature decreases with height, the sound waves sent out along paths that are somewhat angled upward end up traveling along even steeper paths and thus will not reach observers on the ground several kilometers away (Fig. 3-3a).

The wind speed usually increases with height. In such a normal situation, if sound is sent in the direction of the wind, it tends to nosedive to the ground and thus can be heard (Fig. 3-3b). However, if it is sent opposite the wind, it tends to follow a path that bends up into the air and cannot be heard.

In some Civil War battles, the commander was upwind of the battle when there was a significant increase in wind speed with height. The commander is said to have been in an acoustic shadow. Even stranger were situations where sound waves were redirected upward by the temperature effect but then were redirected downward by the wind effect, ending up back on the ground far from the battle. So, distant soldiers heard the battle but not soldiers who were reasonably close to it.

3.24 Trawling bats and the acoustic mirror effectJearl Walker www.flyingcircusofphysics.comApril 2007 Bats locate lunch by emitting a burst of ultrasound and then detecting the echo of the sound from its prey, perhaps a moth. When the moth is flying reasonably far from the ground and vegetation, the bat has an easy time of detecting the echo and then altering its flight to intercept the moth. However, if the moth is near vegetation, the bat can receive a confusing clutter of echoes that mask the echo from the moth, and so the moth can go undetected. Some bats hunt (trawl) for prey by flying over water. If the water surface is flat in front of the bat, the water reflects the incoming sound away from the bat, decreasing the clutter sent back to the bat. If a moth is also flying over the water, the echo from it back to the bat can then easily be distinguished, allowing the bat to home in. However, such trawling for prey may have an additional advantage. Sound reflects from the prey not only directly back to the bat but also to the water surface between the prey and the bat. There some of the sound happens to reflect from the water to the bat. So, the bat receives an even stronger echo than if it detected only the sound reflecting directly to it from the prey. Such additional echo is said to the acoustic mirror effect. This strengthening of the echo should allow a bat to detect prey from a greater distance than if the prey were flying well above the water or ground. Indeed, Bjorn M. Siemers, Eric Baur, and Hans-Ulrich Schnitzler of Tubingen University in Germany recently demonstrated that this acoustic mirror effect increases the detection distance by 50%. Now, of course, you cannot interview a bat to determine when it first detects a target. They just don’t talk very easily, kind of like of me at a party. However, you can detect and analyze the signals they repeatedly send out. Each goes out and then returns, and then the next signal goes out. When the bat happens to receive an echo from a possible prey, it noticeably changes the next signal it sends out in order to locate the prey. Thus, the researchers could determine the detection distance by measuring the distance between a bat and a prey when the bat changed its signal. Just think about this for a moment: A bat, with a tiny brain and a complete inability to work even the simplest algebraic calculation, can analyze the physics of a complex echo that would just be noise to you and me. Moreover, trawling bats have learned that lunch is easier to find if they fly over flat water. If you and I would had to be this smart, we would just starve to death.

3.27 Cocktail-party effectJearl Walker www.flyingcircusofphysics.comOctober 2006 The cocktail-party effect is a name given to your general ability to pick out a conversation in the midst of many sound sources, such as other partygoers. The fact that you hear with two ears instead of one is certainly involved, because the signal from one ear may be delayed from the signal from the other ear. For example, if a speaker is on your right side, your right ear receives a spoken word from the speaker slightly before your left ear. Based on experience, your brain can use the difference in arrival times to determine the direction of the speaker amid the noise in the room. Also, your ability to make sense of a sentence after hearing only portions of it (you mentally fill in missing sounds and even words) can also help. And your ability to read the lips and body language certainly helps. (If the speaker throws her hands upward while scowling, she is certainly not telling a joke.) However, recent research suggests that the cocktail-party effect also depends on whether you mentally focus on the speaker. If you know where the speaker is in front of you, you can direct your attention to her and exclude much of the background sounds from other people and from sound bouncing off their bodies, the walls, and the ceiling. All that extra noise is still coming into your ears and its information is still being sent to your brain, but you tend to ignore it and concentrate on the speaker's voice. In contrast, if you don't know where the speaker is located and thus cannot focus on the speaker, you are less able to sort the speaker's voice out from the noise. You may have noticed this result if you have been in a crowded party when someone calls out your name and begins talking to you before you can locate the person in the surrounding crowd.

3.41 Bottle music --- tapping, buzzing, and blowingJearl Walkerwww.flyingcircusofphysics.comJan 2009 There are at least three distinct ways that a bottle, such as a beer bottle or a jug, can be played as a musical instrument.

1. You can tap the bottle on its side so that the bottle oscillates. The frequency you hear then depends on the shape and thickness of the bottle’s wall, the amount of liquid inside the bottle, and (to a lesser extent) the length of the air column between the liquid and the open end. Increasing the liquid tends to decrease the frequency because the liquid’s mass decreases the rate at which the wall can oscillate. Here are two of the most interesting videos showing this type of bottle playing: a rollerblader rolls past an array of bottles while a projection from each rollerblade strikes the bottles one after another.

You hear a sound pulse emitted by each bottle as it is struck but the sensation of music comes from the timing of the pulses --- the frequencies are subjective frequencies because they are created by your brain in interpreting the series of noise pulses as the bottles are hit one after another. Each impact emits a sound pulse but the time between the successive impacts is too small for you to perceive the individual pulses. Instead, you perceive the frequency of the impacts, that is, how many impacts and pulses occur per second.

2. A second way to play a bottle is used in jug bands (the ones that actually use a jug). The player holds the open end of an empty jug about a centimeter in front of his lips and then pushes air through his tensed lips, producing a. buzzing sound. The jug amplifies the sound so that it can be heard directly by the audience or picked up by a nearby microphone. The jug acts as a resonating chamber. If sound of a particular wavelength entered the jug, resonance would be set up like in an organ pipe, that is, the sound waves would overlap so as to reinforce one another, producing a loud sound. The jug player does not set up such pure resonance but the sounds of his buzzing still undergo partial reinforcement so that the sound that leaks out of the jug is louder than the performer would produce without the jug. Here is a video showing Tommy Hall playing a jug in the legendary psychedelic band The 13th Floor Elevators in about 1965: http://www.youtube.com/watch?v=cYh5oMDlWwQ

3. The third way to play a bottle is the most common way --- you blow across the open top of the bottle. Many videos show this technique but here is one of my favorites:

When you blow across the top of the bottle, you push the air in the neck of the bottle slightly down the neck, compressing the air in the body of the bottle. That sets up oscillations of the air in the neck and the air in the body.

The situation is often likened to a block oscillating on one end of a spring whose other end is fixed in place. The block is initially at the equilibrium point, with the spring neither compressed or stretched. If you push the block so as to compress the spring and then release the block, the spring pushes the block back toward the equilibrium point but overshoots that point. Thus the spring becomes stretched and begins to pull the block in the opposite direction to return it to the equilibrium. Again that point is overshot and the spring is again compressed. The cycle is then repeated.

With the bottle, the air in the neck acts like the block and the air in the body of the bottle acts like the spring. When the block air moves downward, it compresses the spring air, which then pushes the block air back up the neck. However, the block air overshoots the equilibriumpoint and moves up a bit too far. The air pressure in the spring air is then lower than the external air pressure and the pressure produced by your blowing, and thus the block air is pushed back down the neck and the cycle is repeated. As long as you blow across the top of the bottle, the block air oscillates up and down. The motion produces variations in the air pressure just outside the bottle, causing a sound wave to travel from the bottle.

This arrangement of oscillating spring air and block air is said to be a Helmholtz resonator after Hermann von Helmholtz who studied sound and its perception in the mid-1800s. The frequency you hear depends on the amounts of spring air and block air and on the cross-sectional area of the bottle’s neck. The dependence on those parameters is largely due to the easy or difficulty of moving the block air in the neck.

You can vary the frequency by changing the amount of liquid within a bottle (thus changing the amount of spring air) or by choosing a bottle with a different size or shape. As you can see in the following links, setting up a band with various Helmholtz bottle resonators is fun and very popular, especially when the contents of the bottles must first be consumed.

The wineglass has thin walls so that when I rub a wet finger around the rim, I can easily cause the wall to oscillate, which sends out a sound wave. The frequency of the oscillations (and thus of the sound waves) depends on the depth of wine or any other liquid in the glass. In general, adding more wine makes the oscillations more sluggish and thus lowers the frequency.

Of course, other thin-walled wineglasses will do the same but the delight of this particular wineglass is that marks have been put on the wall showing me what the wine level should be in order to get a particular note. For example, in my photograph, I have added enough liquid (stout, not wine, for me) to the level marked G# so that the oscillations produce a G-sharp note.

Here is a link to a video produced by Uncommon Goods to demonstrate their wineglass musical capabilities.

From The Flying Circus of Physics book, here is my explanation for the physics of a musical wineglass. As your finger rubs against the rim, the finger and rim are continually undergoing sticking and slipping. During the sticking phase, the rim is pulled very slightly in the direction of your finger’s motion, distorting the rim’s shape. During the slipping phase, the rim breaks free of your finger and attempts to regain its original shape, but it ends up oscillating. The strongest oscillation is said to be resonance, in which the rim oscillates as shown in the overhead view of this figure:

Here is a slow-motion video showing the rim oscillations being driven acoustically by intense sound waves instead of a rubbing finger. Eventually the oscillations are large enough to break the glass.

In playing a wine glass, the oscillation pattern follows your finger around the rim, producing a pulsation to the sound (it comes and goes with a frequency of a few hertz, depending on the speed of the finger on the rim). The frequency at which the rim pushes on the air and the frequency that you hear are roughly proportional to the rim thickness and inversely proportional to the square of the glass’s radius at the open end. Thus, generally the frequency is higher for a thicker rim and smaller radius. If you add liquid to the glass, you lower the resonant frequency because the liquid’s mass decreases the rate at which the glass wall can oscillate.

Some musicians are skilled at playing music on an array of glasses containing various levels of liquid. Here is my favorite example:

3.43 Pub trick --- moving match sticks on a glass rimJearl Walker www.flyingcircusofphysics.comMarch 2008 In the video link given below, we see two match sticks balanced across the rim of a glass of water (or whatever beverage you like). The challenge is to make the match sticks move without touching them or the glass with anything, shaking the table, or blowing on the matchsticks.

The video also shows the solution: You need a second, identical glass with an identical amount of water. With a slightly wet finger, you rub the rim of the second glass to set up stick and slip, in which your finger rapidly switches between sticking to the rim and sliding along the rim. When your finger sticks, your forward push on it distorts the rim slightly. When your finger slides, the distortion is suddenly released and the rim oscillates, until your finger next sticks.

If you slide your finger at a fairly steady pace, you build up a strong oscillation of the rim. You can see a slow-motion video of a similar oscillation of the rim at this link, but the oscillation is being driven by a sound source rather than stick-and-slip motion of a finger:

When the glass wall oscillates, it pushes against the air to send out a sound wave. The frequency that you hear and the frequency of the oscillation are roughly proportional to the rim thickness and inversely proportional to the square of the glass’s radius at the open end. The water shifts the frequency downward because its mass decreases the rate at which the glass wall can oscillate.

Now here’s the point to the bar trick: If the two glasses are identical and contain identical amounts of water, then they should oscillate at about the same frequency. Thus the sound wave from glass 2 can cause glass 1 to oscillate (the glasses are said to be in acoustic resonance), which in turn causes the match sticks to jump about.

So, a bar room bet can be soundly won on the basis of acoustic resonance.

3.44 Shattering a wineglass by singingJearl Walker www.flyingcircusofphysics.comNov 2007 Can someone sing so that the sound waves cause a wineglass to shatter? In The Flying Circus of Physics book and in all my classes about sound, I have argued that it is possible but probably too demanding. However, videos now on the web prove me wrong. In fact, some singers can apparently shatter a wineglass with little effort, which must make them dangerous at a combination singing and wine-tasting party.

Here is the physics. The rim of a wineglass can be made to oscillate in a pattern in which portions oscillate radially inward (toward the center of the open mouth) and outward (away from the center), as shown in slow motion at this link:

In between there are points that undergo little or no oscillation. This pattern of strong oscillations and no oscillations is said to be the fundamental pattern. The oscillating parts push to and fro on the surrounding air, producing a sound wave, which you can hear. The frequency (or pitch) of the sound matches the oscillation frequency of the rim. You can easily set up the pattern and hear the oscillation frequency if you snap a finger against the rim.

If the rim oscillates vigorously enough, the strain put on the glass can shatter it, especially if there is a flaw (a microfracture or impurity) in a region of oscillation. However, if the glass is thick, such fracture is unlikely because the rim is too stiff to move very much.

The rim can also be set in motion if someone sings with a sound wave that has a frequency matching the oscillation frequency of the rim. Such a match is said to be resonance. Although certain legendary singers of the past were said to be able to shatter thin-walled wineglasses by singing, there was no tangible proof.

In more recent times physicists have attempted to set up such a shattering demonstration but without success unless they amplified the voice. There are seemingly two problems: The voice must be loud to produce a vigorous resonance, and the voice must be held at the correct frequency for at least a few seconds. If the voice wanders around the correct frequency, then resonance probably will not occur long enough to shatter the glass. So, a singer in some death metal band (where hitting the right note is carefully avoided) would never be able to shatter glass (even though such a demonstration would be appropriate in a metal concert).

Here is one of the links to videos of glass shattering by singing. Note that the woman taps the glass to hear the resonant frequency so that she knows how she should sing. Notice also the drinking straw. When she hits resonance, the oscillations of the glass cause the straw to bounce around, signaling her that she is at the right frequency.

I have problems with this video. (1) The rim is against the table, so how could it oscillate sufficiently to break? (2) How could the base of the glass snap off? Sure, the stem can be made to oscillate in resonance, but the required frequency will not be the same as for the rim of the glass. (3) If the television director does not know exactly when the glass is going to break, wouldn’t he keep the camera continuously pointing at the glass instead of cutting away for a face shot?

So, I don’t think the sound from the woman’s singing broke the glass. Rather I think, on the director’s cue, someone turned on an intense beam of ultrasound that quickly shook the glass apart without having to set up resonance. What do you think?

When you pull on a finger to crack a knuckle, you widen the space between the bones that form the knuckle and also decrease the width of the knuckle cavity. That cavity contains an initially thin layer of synovial fluid separating the bones. If the pull on the finger is done with enough force, the sides of the cavity can snap outward, increasing the width of the cavity and decreasing the pressure within the synovial fluid. This sudden pressure decrease allows one or more gas bubbles to form from the gas, primarily carbon dioxide, that is dissolved in the fluid. The sudden appearance of bubbles, called cavitation, sends a pressure pulse through the fluid, the knuckle cavity, and out into the air. When the pulse reaches your ear, you hear a cracking sound. To repeat this performance, you must allow 15 to 30 minutes for the cavity to recover its initial shape, for the synovial fluid to be squeezed back to a thin layer between the bones, and for the gas to be redissolved into the fluid. Until then, you need some other bad habit to annoy people around you.

x3.50 Killer shrimpJearl Walker www.flyingcircusofphysics.comOctober 2006 In the book I explain that a certain type of shrimp kills its prey by snapping shut one of its claws to send out a lethal sound wave. High-speed photography reveals that the snapping of the shrimp claw is really a double punch. A strong sound wave is generated by the mechanical crash of the claw and then a second, sometimes even stronger, sound wave is generated by the collapse of the bubbles produced by the mechanical crash. This double punch can be devastating to the shrimp's prey but, strangely, it does not seem to hurt the shrimp. That is good, of course, because it would be embarrassing if the shrimp knocked itself out every time it knocked out its lunch.http://www.youtube.com/watch?v=XC6I8iPiHT8 video with sound of the shrimphttp://asa-sp.ims.nrc.ca/Archives/GalleriesPast.html#Newport%20Beach you need to scroll down· Patek, S. N., W. L. Korff, and R. L. Caldwell, “Deadly strike mechanism of a mantis shrimp. This shrimp packs a punch powerful enough to smash its prey’s shell underwater,” Nature, 428, 819 (22 April 2004)· “Mantis shrimp deliver double whammy,” Journal of Experimental Biology, 208, ii (??month 2005)· Patek, S. N., and R. L. Caldwell, “Extreme impact and cavitation forces of a biological hammer: strike force of the peacock mantis shrimp Odontodactylus scyllarus,” Journal of Experimental Biology, 208, 3655-3664 (2005)

Want more references? Use the link at the top of this page.x

3.53 Snap, crackle, and popJearl Walkerwww.flyingcircusofphysics.comNovember 2013 Rice Krispies, a popular breakfast cereal in North America, consists of toasted, puffed rice grains. When these grains are placed in milk, they make a crackling sound, hence the “snap, crackle, and pop” slogan long used by the manufacturer to market the cereal. Here is one of TV commercials I watch as a child:

And here is a video in which you can hear the sounds of Rice Krispies in milk. (The video is long but you can get the idea within a few minutes. Well, maybe you might find the sounds comforting, in which case you can run the entire video as a kind of Zen thing.)

Each grain is brittle and under stress; that is, the various parts of the grain pull tightly on one another. When a portion becomes wet, its rigidity decreases and the portions pulling on it rip it apart. This sudden motion causes momentary oscillations, which produce a faint pulse of sound that is more of a crackle than a snap or pop. If you eat this type of breakfast cereal, keep in mind that the sounds you hear are the dying shrieks of puffed rice grains.

x3.54 Shock waves from a volcano and a rocket launchJearl Walkerwww.flyingcircusofphysics.comJuly 2011 The Iceland volcano Eyjafjallojokull erupted in 2010 and disrupted air travel across much of Europe because of the dust it dispersed. I have previously discussed the terrific sparking (“volcanic lightning”) that accompanied the smoke, dust, and ash plumes. Here is another effect: the volcano would occasionally undergo a series of explosions that send shock waves through the plumes. Which for the quickly moving dark bands in this video:

There are old reports of similar dark bands racing through normal clouds when heavy artillery was fired. Considering how common artillery firing has been in the last two centuries, the rarity of such observations suggest that the lighting conditions must be crucial for the bands to be visible.

The bands are not bands of dust and ash racing through the plumes, as if caught up in a huge, rapidly moving wind. The dust and ash are rising much more slowly than that, as you can tell from the plume movement. Rather the bands are an optical effect caused by the shock waves --- waves of high pressure that move through the air at the speed of sound. These waves refract (redirect) the light rays that pass through them. At a given instant, the light passing through part of the waves is spread out by the refraction, and so that light is dimmer than it should be when it reaches us (the video camera). The light passing through an adjacent part of the waves might be concentrated, and so that light is brighter than it should be. We can see this dimming and concentrating because the camera is so far from the volcano than the waves pass through a small viewing angle. Were the camera much closer or farther away, the bands would be too wide or too narrow to see.

Rocket launch

A beautiful array of shock waves was produced when the Solar Dynamic Observatory was launched in February 2010. The boost rocket (an Atlas V) was traveling faster than sound at the altitude where it passed through cirrus clouds.

The shock waves emitted by the rocket were momentarily visible as they raced through the clouds, distorting our view of them. Well, I think that is the explanation. The alternative is that the shock waves were visible where they caused condensation of water drops from the water vapor in the air, similar to the visible shock waves that supersonic aircraft can produce.

The waves also wiped out the sundog display of color that was to the right of the rocket’s path. That coloration is due to the dispersion of sunlight as it passes through ice crystals. These crystals are short and six-sided and flat on top and bottom. They tend to drift with a flat side down. When sunlight passes through one of the six sides and out the adjacent side, the light is spread out according to wavelength as a prism can spread out colors.

The orientation of the crystals giving the sundog was disrupted by the shock waves, making the sundog disappear. The white column that appears to the left of the rocket’s path is a related optical displayed that apparently is due to the shock waves causing the flat ice crystals to spin like a top while tilted from the vertical by an angle between 8 and 12 degrees. As sunlight travels through the spinning crystals, it can be bunched to give a white bright streak in the sky. Although lots of different atmospheric streaks, arcs, and spots have been studied over the years, this particular display had never been seen previously.http://science.nasa.gov/science-news/science-at-nasa/2011/11feb_sundogmystery/

x3.54 Photo of a shock wave shed by an aircraftJearl Walker www.flyingcircusofphysics.comJune 2007 Several of my students and visitors to this web site have asked me about the web-available photos showing the shock wave of a supersonic aircraft. A number of links to the photos are given below. However, at least two of the photos are fakes. Can you spot them and explain why they cannot be true?

Here is the physics, as discussed in The Flying Circus of Physics and in Fundamentals of Physics (the textbook I write): When an aircraft travels through air, it pushes air molecules out of the way, which causes a variation in the air pressure. This pressure variation travels away from the aircraft as a sound wave.

If the aircraft is flying faster than the speed of sound at that altitude (the aircraft is supersonic at that altitude), these waves move slower than the aircraft and bunch up to form a cone with its tip (apex) at the aircraft. The surface of that cone is the shock wave. As it sweeps through a point, the air pressure suddenly increases, then suddenly decreases, and then returns to its initial value.

If the air humidity is fairly high, the sudden decrease in air pressure can cause water vapor in the air to form water drops. However, the drops are short lived because they evaporate as soon as the air pressure returns to its initial value. So, if the humidity conditions are right, a photograph of a supersonic aircraft can show a fog that seems to travel along with the aircraft, either at its nose or at some protrusion in the passing air (such as at the tail section). The attachment is just an illusion because water drops continuously form and then almost immediately disappear as the airplane pushes its way through the air.

The aircraft does not have to be supersonic to produce the fog. Even at speeds just below the speed of sound, if the humidity is right, the pressure variations generated by the aircraft might still be sufficient to produce a fog.

Here are several images of shock-wave condensation produced by aircraft that are either supersonic (faster than sound) or almost supersonic. At least two of them are fake. Can you spot them and explain what is wrong?

3.54 Shock waves from large explosionsJearl Walkerwww.flyingcircusofphysics.comOctober 2010 The energy released in a huge explosion can heat the air so rapidly that the air expands faster than the speed of sound, sending out a shock wave. As this wave moves outward through the surrounding air and along the ground, it causes an abrupt increase in air pressure. If you are fairly near a large explosion, you will first see it and then, slightly later, hear it when the shock wave reaches you. In some of the videos listed below, you can see the video camera shake as the shock wave hits it, well after we can see the explosion.

In the following video of a very powerful explosion, the motion has been slowed sufficiently that we can see distortion in the light that passes through the shock wave. Inside and outside the hemispherical shock wave, the background is fairly clear, but at the shock wave surface on the left, top, and right sides, the view of the background is noticeably distorted.

Normally when we look at a certain spot in the background, we intercept light rays that come to us directly from that spot. However, when a shock wave lies along the path, the rays are bent (refracted) into other directions of travel because of the abrupt change in the density of the air at the shock wave. The rays that we then intercept come from other spots in the background, and thus our view of the background is distorted. You may have seen similar distortion in the haze over a heated surface, such as a road in bright sunlight.

In normal circumstances, however, the expansion of a shock wave is too rapid for us to distinguish any visible distortion. Then our best chance of seeing the wave is by the effect it has on water or dirt. In the following photo (Official U. S. Navy Photograph, USNHC # DN-ST-85-05379, by PHAN J. Alan Elliott. From www.navsource.org/archives/01/61h.htm) , the shock wave produced by a large ship artillery can be seen on the water surface.

In these next two videos, the shock wave produced by a large explosion can be seen in the disturbance of the ground dirt.

Even larger explosions were produced with atomic bombs back in the days when the bombs were still being tested. In the following video, toward the end, you can see the ground-level shock wave of an atomic explosion race over the trench in which soldiers were crouched.

One peculiar feature of a very large explosion is that as the shock wave travels outward, the pulse of high pressure gradually transforms so that the leading edge is high pressure and the trailing edge is low pressure. On a graph of pressure versus distance, the plotted curve resembles the letter N and thus the pulse is sometimes referred to an N-shaped pulse.

In films taken during ground level tests of atomic bomb, you can see the effect of the N-shaped pulse of the shock wave as it sweeps through trees or mock towns. The trees and debris are first blown away from the blast site and then back toward the blast site.

3.63 Whispering bench in New York City's Central ParkJearl Walkerwww.flyingcircusofphysics.comApril 2015 Some concave architectural surfaces have a delightful acoustical effect. If a friend stands at one end of the surface and softly whispers, you can clearly hear the words at the opposite end. The most famous example is the whispering gallery in the dome of St. Paul’s Cathedral in London. The walkway just below the dome is circular with a radius of about 32 meters. When my wife leaned her head near the wall and whispered, I could clearly hear her words on the opposite side of the circle in spite of the general noise coming up from the crowded main floor. When she, instead, faced toward me and attempt to send her words directly along a diameter to me, I could not hear her.

When someone whispers near such a curved wall, the sound waves tend to cling to the wall by reflecting over and over again as they travel around the curve. Here is a sketch from an overhead view:These clinging waves are called surface waves or Rayleigh waves (after Lord Rayleigh who first explained the effect in 1904). The waves cling better for shorter wavelengths (higher frequencies), which is what is emitted when someone whispers.

A number of parks now have whispering benches where you and a friend can experience this clinging effect. One of these is in Central Park in New York City. If a friend sits at one end of this long curved bench and whispers along the wall, the multiple-reflected sound waves travel along the bench to your ear at the other end of the bench. Provided your ear is next to the bench wall and in the sound zone, you can hear the sound waves. If you move your ear outward from the wall, you then move out of the clinging waves and can then no longer hear the whispering.

A whispering bench can be a romantic way of exchanging messages of endearment that cannot be overheard by a third person standing near the bench. But if that person sits down on the bench, the sound waves are blocked and the romance disappears. (Isn’t that always the effect of a third person on romance?)

x3.65 Musical echoes at a Mayan pyramidJearl Walker www.flyingcircusofphysics.comNovember 2006 In The Flying Circus of Physics, I describe how a handclap at the base of the ancient Mayan pyramid at Mexico's Chichen Itza produces a drawn-out musical echo instead of just a single echo that simply repeats the handclap sound. Here is a photo of the site:http://www.whatmexico.com/phototour/chichen-itza-ruins.htmlThe reason has to do with the fact that the sound waves reflect head-on from the lower steps but obliquely from the higher, more distant steps. So, the pulses from the lower steps reach you, one after another, at a certain rate, which you hear as a certain frequency. Shortly later, the pulses from the higher steps reach you, one after another, at a lower rate (because of the oblique path), which you hear as a lower frequency. Thus, the echo begins with a higher frequency and ends with a lower frequency. In 1693, Christian Huygens, a famous figure in the history of optics, described a similar experience in the garden of the Chantilly de la Cour in France. The sound from a water fountain reflected to him from a large stone staircase, giving him an echo at a certain frequency. However, this echo is due to a continuous source of sound (the fountain) instead of a pulse of sound (a handclap).

3.66 Echoes at rock art sitesJearl Walker www.flyingcircusofphysics.comNovember 2006 Rock art is art that has been left on rock walls by ancient people. It often depicts animals, such as deer, that the people probably hunted. In recent times, researchers have realized that the site of rock art is often a point where strong echoes can be heard. If you stand back away from the art and, say, clap your hands, the echoes returning to you can give the illusion that the sound originated from the animals in the art. Moreover, if you strike two stones together, the echoes resemble hoof beats, as if the animals are running. Some rock art can be found in the caves of southern France, at points where a handclap or yell produces strong echoes. The reflecting sound waves briefly travel through one another, from one end of a passageway to the other, and set up a temporary acoustic resonance, somewhat like you might set up while singing in a shower stall. Such resonance may have been magical to ancient people, provoking them into drawing animals and signs on the walls to mark those special points in a cave. If the cave passageway was too tight, rough, or wet for extensive drawings, the point was marked with a red dot (usually ochre, which is a mixture of clay and ferric oxide). Such a dot was effectively a sign saying, "This is a magical point. Chant or hum here to contact the greater spirits."

3.69 Booming sand dunesJearl Walker www.flyingcircusofphysics.comOctober 2006 Recent research indicates that avalanches on sand dunes can boom if the jostling of sliding sand grains becomes synchronized. The sound frequency is related to the depth of the sliding layer---greater depth means lower frequency. However, booming is fairly rare because the ability of the grain motion to become synchronized depends on the surface of the grains. The booming sand has acquired desert glaze, which is a silica gel layer. If the grains are made to slide against one another repeatedly, this glaze wears off and then the sound production ceases. Reasonably, this dependence on the surface must mean that the ability of the sliding to become synchronized depends on the friction of sand grain rubbing on sand grain.Here is the web page for Stephane Douady where he offers sound bites of the sand sounds, but I cannot get them to play. You can give them a try.http://www.lps.ens.fr/~douady/

3.77 Culvert whistlersJearl Walkerwww.flyingcircusofphysics.comJune 2012 If you clap your hands at one end of a culvert or long pipe, you will hear an echo that “zings.” That is, it starts at the highest frequency and quickly descends to the lowest frequency. These special echoes have been dubbed whistlers. You can also hear a whistler if a friend claps hands at the far end of the culvert. My favorite example of whistlers is demonstrated at the Exploratorium in San Francisco, where I can clap my hands at one end of a very long pipe. Why does a whistler occur? That is, why would an echo’s frequency change?

The whistler is due to a complicated resonance in which sound waves reinforce one another. However, here we can get by with a simple explanation. Let’s assume that your friend’s handclap, which emits a pulse of sound, is near the center of one end of the pipe and that the pipe has a length L. The sound can reflect from the sides of the pipe in many ways. For example, it might reflect at distance L/2 (halfway down the pipe) and thus make only one reflection.

More reflections require that the sound takes a more zig-zag path down the pipe, and thus it travels the length of the pipe more slowly. So, you first hear the single-reflection echo, then the double-reflection echo, and so on. The frequency you perceive is the frequency at which these echoes arrive at your ear. The first sequence of echoes (which requires only a few reflections) is rapid, and so you hear a high frequency (the z of zing). The later sequence of echoes (more reflections) is less rapid, and so you hear a lower frequency (the ing of zing). The limit is set by the echoes that reflect almost directly across the diameter of the pipe and thus hardly travel down the pipe.

The story is about the same if you listen for the echoes of your own handclap. However, this time the sound must reverse its direction of travel at the far end. That occurs for both a closed end (the culvert has a wall or cap there) or an open end. The latter may be surprising—when sound reaches the open end of a pipe, the abrupt transition to the open air causes some of the sound to travel back through the pipe. We say that some of the sound reflects at the open end.

3.82 Strange ice soundsJearl Walker www.flyingcircusofphysics.comNovember 2006 When a thin layer of ice lies over a pond, you might be able to hear a strange sound if you toss a stone out over the ice. Just after the stone hits, you might hear a slightly prolonged sound resembling the chirp of a bird. Why don't you hear just a single pulse of sound? Neil Basescu of Westchester Community College (Valhalla, New York) told me how he happened to generate this chirping sound and then how he worked out its source. The stone's impact on thin ice causes the ice to fracture at the point of impact and in the surrounding area. Both the impact and fracturing send out sound waves through the air and the ice. The speed of sound is higher in the ice, and so that sound reached him first, and then slightly later, the sound through the air reached him. Thus, the total sound that come back to him was noticeably longer lasting than what he would have heard had the stone merely bounced off (thicker) ice. x

3.82 Mysterious sound of stone hitting an ice-covered pondJearl Walkerwww.flyingcircusofphysics.comJanuary 2013 Here is a mysterious sound effect from an ice covering on a pond. Someone throws a stone out on a pond that is covered with a moderately thick layer of ice. As the stone lands, you don’t hear just a thud but a ping.

In the early days of the Flying Circus of Physics web site I posted the following description of this sound.

“When a thin layer of ice lies over a pond, you might be able to hear a strange sound if you toss a stone out over the ice. Just after the stone hits, you might hear a slightly prolonged sound resembling the chirp of a bird. Why don't you hear just a single pulse of sound?

“Neil Basescu of Westchester Community College (Valhalla, New York) told me how he happened to generate this chirping sound and then how he worked out its source. The stone's impact on thin ice causes the ice to fracture at the point of impact and in the surrounding area. Both the impact and fracturing send out sound waves through the air and the ice. The speed of sound is higher in the ice, and so that sound reached him first, and then slightly later, the sound through the air reached him. Thus, the total sound that came back to him was noticeably longer lasting than what he would have heard had the stone merely bounced off (thicker) ice.”

Well, that is what I wrote in the old posting. Now that I can hear the sound myself, I want to modify the explanation. Each time the stone hits, there is a ping, not just two pulses of sound, as I would expect for one pulse through the air and another one through the ice. I think that the pinging is due to multiple emissions into the air by sound traveling through the ice layer.

We first hear the dull thud of the impact: a sound pulse travels from the impact directly through the air to the microphone. The impact also sends a pulse through the ice layer. If the layer has the proper thickness, the pulse bounces up and down between the top and bottom of the layer as it travels away from the impact point. Each time the pulse bounces off the top, some of the sound leaks out into the air. So, after the initial dull thud, we hear a series of pulses, one from each time the internal pulse bounces from the top of the layer.

The frequency we perceived in the ping is the frequency at which the pulses are emitted from the surface. If we measured the frequency and looked up the speed of sound in ice, we could work out the thickness of the ice layer. If the layer is too thin, the internal pulse cannot bounce up and down. And if the layer is too thick, the internal pulse may not have chance to bounce from the bottom and then back up to the top.

If you observe this effect or have another explanation, please let me know. In meantime, I shall be throwing stones on every ice-covered pond that I can find.

x

x3.83 Sounds of puttingJearl Walker www.flyingcircusofphysics.comDecember 2006 A professional golfer has an intuitive feel for putting a golf ball toward the hole. Obviously years of experience and a keen eye for the lay of the green are essential. However, the golfer can also analyze the ball (perhaps subconsciously) via the sound it makes when the putter hits it. Indeed, often a player will test an unfamiliar ball by dropping it onto a hard surface, to hear the ball bounce. What clues lie in such sound? Successful putting requires an exquisite control over the way the ball leaves the putter, both in direction and speed. The direction is obviously important, because putting away from the hole just brings laughter of onlookers. But the speed is also important because if the ball hits the hole at too high a speed, the ball just "bounces out." Usually a golfer describes a "hard ball" as one that shoots off the putter with less control over direction and speed and a "soft ball" as one that leaves the putter more slowly and with more control. Such evaluations are, to be sure, highly subjective but may, on the average, allow a golfer to adjust the putting during a game when the putting has not been very good. In a long drive off a tee, a golfer has three general ways to judge the hardness of a ball. One way obviously lies in the path that the ball takes (the height and distance). A second way lies in the pressure and oscillations on the hands due to the impact. The third way comes via the sound made when the club hits the ball. All three ways are important during a long drive, but only the sound is important during the milder impacts in putting. The impact by a club causes the ball to oscillate much like a bell oscillates when struck. And, just like a bell, a ball tends to oscillate in a certain pattern, said to be a resonance pattern. As the ball's surface oscillates and pushes on the adjacent air, sound waves are radiated from the surface. The frequency of those waves depends not only on the oscillation pattern but also on the materials and design of the ball. Tests indicate that a softer (more compressible) ball tends to oscillate in a broader range of frequencies centered on a lower frequency than does a harder ball. A golfer can hear the difference: The softer ball emits a duller, lower frequency sound (a "thud") while a harder ball emits a sharper, higher frequency sound (a "ping"). In putting, a thud is desirable. If the ball pings, the golfer has a harder ball and needs to hit it more softly, to control how it runs over the green.

3.84 Fizzing in a glass containerJearl Walker www.flyingcircusofphysics.comJanuary 2007 To reduce the splashing when pouring a carbonated beverage (soda, beer, or champagne) into a drinking glass, you can tilt the glass and pour onto the slanted interior surface, so that the stream hits a solid instead of the liquid already in the glass. There is still enough turbulence to create bubbles. Listen to their fizz as they form, merge, and pop open. Although the noise extends over a range of frequencies, you can hear a dominant frequency that shifts as the depth of liquid in the glass increases.

The primary noise of the fizzing is independent of the depth but the noise also creates a weak resonance in the air space between the liquid and the top of the glass. That air space acts as though it were an organ pipe that is closed at one end (at the liquid) and open at the other. The resonant frequency of such a pipe depends on the pipe length---a shorter length corresponds to a shorter wavelength of sound and thus a higher resonant frequency. As you pour in more liquid, the air space in the glass decreases, and so the resonant frequency you hear steadily increases.

3.85 Sound mirrors detecting enemy aircraftJearl Walker www.flyingcircusofphysics.comMarch 2007During World War I, German airships (Zeppelin and Shutte-Lanz) bombed regions around the Thames estuary (southern England) and Humber estuary (northern England). In order to detect the airships before they arrived, the English built an early warning system of sound mirrors that would intercept and concentrate the sound waves of an approaching airship so that it could be heard before it was within normal hearing range. The first sound mirror was simply a hemispherical cavity dug into a chalk cliff on the southeast coast. The sound waves, at least those with wavelengths smaller than the radius of the hemisphere, reflected from the wall of the cavity and passed through the center of curvature (the point that would be the center of the sphere were the sphere complete). At that point, a horn was mounted to collect the waves and send them through rubber tubes to someone listening at the other end of the tubes. The photo here (by sqwasher) shows a smaller concrete version without any of the listening equipment. Although listening for the sounds of enemy airship must have been mind-numbing work because of the background noise that was also reflected into the collecting horn, this early-warning system functioned reasonably well. Moreover, if the listener moved the collecting horn horizontally to the point at which the airship sound was loudest, the direction of the airship could be determined. If the airship headed directly toward the sound mirror, the reflected sound was loudest when the collector was at the center of curvature. If (as was more likely) the airship was off to one side of the direct approach, the sound was loudest at a point on the opposite side of the center of curvature. Several sound mirrors were built during the war, and enemy airships were detected on at least two occasions, allowing several extra minutes of warning. After the war, free-standing concrete sound mirrors were deployed on several English shores. The size was increased so that longer sound wavelengths could be properly reflected to the collecting device at the center of curvature. In 1930, a long curved sound mirror (in the shape of a curved wall) was built at Denge. The wall was designed to collect sound over a wide horizontal range and focus the waves onto a collector. It was capable of detecting aircraft that was 20 or 30 miles away, whereas normal hearing was limited to about 6 or 7 miles. However, by 1935, all the sound mirrors became outdated because radar came into use and shown capable of detecting aircraft that was 40 miles away. You can find similar sound mirrors in the equipment used by bird enthusiasts to hear birdcalls or spies to hear conversions. However, today’s devices are small, portable metal dishes with sensitive electronic microphones placed at the concentration points. Two larger-scale versions are set up in the lobby of the physics building at the University of Florida, where students can listen to whispers from across the width of the large lobby. (Hearing whispers across the domed interior of Saint Paul’s Cathedral depends on entirely different physics. Check out item 3.63 in The Flying Circus of Physics.) Web pages by Andrew Grantham, lots of photos and brief descriptions of the sound mirrors in England and Malta:http://www.andrewgrantham.co.uk/soundmirrors/Excellent review of sound mirrors on the south coast of England by Phil Hide:http://www.doramusic.com/soundmirrors.htmThe Sound Mirrors Project, an artistic venture to send performances across the English Channel, between a sound mirror on the English coast and a sound mirror on the French coasthttp://www.youtube.com/watch?v=qsR3qyJDk0c Sound mirrors from the English coast (in defense against German airships), set to musichttp://www.soundmirrors.org/

3.86 Acoustic sculptureJearl Walker www.flyingcircusofphysics.comJune 2007 The links given below take you to photos of a Madrid sculpture by artist Eusebio Sempere. The sculpture consists of hollow, vertical tubes that form parallel planes. In 1995, R. Martinez-Sala, J. Sancho, J. V. Sanchez, V. Gomez, and J. Llinares of Universidad Politecnica of Valencia, Spain, and F. Meseguer of Campus de Cantoblanco of Madrid, Spain, realized that the sculpture resembled the periodic arrangement of atoms in a crystal. More interestingly, they discovered that the sculpture could affect sound waves much like a crystal can affect x rays.

When x rays are sent into a crystal, they scatter from the planes formed by the atoms in the crystal, in a process known as Bragg scattering. For certain wavelengths of the x rays, the waves scattered by the planes undergo destructive interference in which the crest of one wave overlaps the valley of another wave. With such an overlap, the waves tend to cancel each other, and the x-ray scattering by the crystal is then minimum.

The Spanish researchers reasoned that similar cancellation could occur when waves scatter from the planes of the tubes in the Sempere sculpture. However, the wavelength would have to be different because the spacing between the scattering planes is different. In a crystal, the atomic planes are only 0.1 nanometer apart, and so x rays with a comparable wavelength are required. In the Sempere sculpture, the tubes are 10 centimeters apart. Thus, the researchers used sound waves with wavelengths of about 10 centimeters. As they predicted, certain wavelengths result in destructive interference and a minimum in the sound scattered by the sculpture. A number of researchers are now investigating how other arrangements of hollow tubes can redirect and even focus sound waves.

I don’t think the Sempere sculpture was constructed for its acoustic effect. However, it does reinforce my general observation: Physics is everywhere.

3.87 Sounds of splashingJearl Walker www.flyingcircusofphysics.comJune 2007 If you drop a solid ball into calm water, do you hear a plop or a splash? Surprisingly, the answer can depend on the wettability of the ball’s surface. Thus, you can roughly determine this microscopic property of the surface simply by listening to the ball hitting the water.

When the ball enters the water, the water attempts to flow up over the top surface, to complete the enclosure of the ball. However, the ability of the water line to advance over the surface depends on the surface’s wettability, which is a measure of the attraction or lack of attraction between the molecules in the water and on the ball. For strong attraction, the surface is said to be hydrophilic, and for weak attraction, hydrophobic.

If the ball is hydrophilic and enters the water below a certain critical speed, the water easily flows up over the top surface and closes off with merely a plop. If the speed is greater than the critical speed, the water’s advance over the top surface breaks down into turbulence, which entrains air bubbles. Somewhere along the top surface, the water breaks free of the surface, allowing an air cavity to form above the ball. As the ball descends, the air cavity becomes longer but then it collapses when the surrounding water suddenly flows into it. The motion of that rapid inflow produces a change in the air pressure, which travels outward as a sound wave, the sound of a splash.

If a hydrophilic ball is dropped into water so that it enters with a speed less than the critical speed, you hear a plop. If you then roughen the surface and repeat the drop from the same height, that entering speed may then be greater than the new (now smaller) critical speed and you hear a splash. If you could somehow make the ball very hydrophobic (said to be superhydrophobic), the value of the critical speed is effectively zero, and then you hear a splash for any speed of the ball entering the water.· Eggers, J., “Coupling the large and the small,” Nature Physics, 3, No. 3, 145-146 (March 2007) · · Duez, C., C. Ybert, C. Clanet, and L. Bocquet, “Making a splash with water repellency,” Nature Physics, 3, No. 3, 180-183 (March 2007)

3.88 Musical roadsJearl Walker www.flyingcircusofphysics.comOct 2008 Road noise is generated by the impact of car tires on the road and the resulting flexing, distortion, and vibration of the tire wall and suspension system of the car. You can often hear a change in the noise when the road surface changes, as from concrete to blacktop, or from smooth to rough. In many places, a rough texture is part of the road design to alert a driver to a dangerous curve or to the side of the road. The rough texture may cause the steering wheel to oscillate slightly, so that the driver both hears and feels the alert.

As a special treat, some roads have recently been fitted with grooves or ridges, each extending across the road width, such that the noise created by a passing car reproduces a musical passage. For example, for a while the road music of Avenue K in Lancaster, California, was the opening theme music of the old television western about The Lone Ranger, a masked man who righted wrongs while riding on a great stallion and shooting bullets made of silver. More sophisticated listeners know the music as a passage from the William Tell overture by Gioachino Rossini. Here is one of several links in which you can hear the Avenue K road music:

http://www.youtube.com/watch?v=BYO81ZRVXKU&NR=1Road music consists of a series of frequencies, or musical notes, but these frequencies are not the oscillation frequencies of the tires or car as in normal road noise. Rather, they are subjective frequencies because they are created by your brain in interpreting the series of noise pulses that are emitted as the tires hit the grooves one after another. Each impact emits a sound pulse but the time between the successive impacts is too small for you to perceive the individual pulses. Instead, you perceive the frequency of the impacts, that is, how many impacts and pulses occur per second.

The road design of Lancaster assumes that the car is driven at the speed limit of 55 miles per hour (88 kilometers per hour). Then, to produce a frequency of, say, 500 hertz, a fairly low note, the spacing between grooves must be about 4.9 centimeters, so that the time between impacts is 2.0 milliseconds. You cannot distinguish sound pulses separated by 2.0 milliseconds. Instead, what comes up to consciousness is the frequency of the pulses, which is the inverse of the time separation. That is, you perceive a frequency of 500 hertz. To produce twice that frequency (1000 hertz), the groove separation must be half as much (2.4 centimeters), which produces pulse separations of 1.0 millisecond. Thus, a higher frequency requires more closely spaced grooves.

The same idea is behind vinyl records, which some music lovers prefer to modern digital recordings. In a vinyl record’s groove, the music is recorded in a series of bumps with the frequency of the music set by the spacing of the bumps. The record is played by rotating it at a certain speed on a turntable so that the bumps collide one after another with a stylus (the “needle”). Each collision compresses a crystal in the stylus and generates an electrical signal, which is amplified and then relayed to a speaker to be part of the music. You interpret the frequency of those signals (the number per second) as the musical notes.

Generating road music is a bit like playing a record with two styluses, because the rear tires hit each groove after the front tires hit it. However, with the car moving at 55 miles per hour, the time delay is less than 0.10 second and may not be noticeable.

Of course, if a musical road were driven backward, the music would be played backward. Such reversal would be especially interesting for some of the Beatle songs on “the white album” because of a 1969 rumor that intrigued Beatle fans world wide, including me. The rumor claimed that by playing some of the songs backward and at a slower speed, the phrase “Paul is dead” could be heard. According to the rumor, this meant that Paul McCartney had died in a motoring accident according to “A Day in the Life” on The Sgt. Pepper album:

He blew his mind out in a carHe didn’t notice that the lights had changed

The rumor claimed that Paul had been secretively replaced by someone resembling him so that the band could continue.

These days, the Beatle songs are on CDs, which cannot be played backward to listen for hidden messages about Paul. However, if one of the songs were recorded in road groves, maybe you would hear the message of “Paul is dead” if you drove a car backward along the road. Well, if you actually did drive the car backward at 55 miles per hour, maybe you would hear the words, “You are dead,” as you would certainly quickly be.

As for the musical road in Lancaster, the residents soon had their fill of it, charging that the road noise sounded like --- well, ah, --- road noise. Alas, their street has been resurfaced to eliminate the grooves, meaning that The Lone Ranger no longer rides in Lancaster, California.

3.89 Whoopee cushionsJearl Walkerwww.flyingcircusofphysics.comMarch 2009 A whoopee cushion is a rubber device resembling a balloon, with an extended flat tube on one side. You inflate the cushion by blowing into the tube as you would inflate a balloon. Once the cushion is inflated, the cushion’s curvature naturally flexes the tube so that air does not easily escape through it. So, the inflated cushion can be left on a chair as a practical joke. When someone happens to sit on it, the person’s weight crushes it, forcing air out through the tube, which produces very rude and embarrassing noises that are commonly associated with a toilet.

Here is a link to an assortment of whoopee cushion sounds collected by Professor Trevor Cox of the University of Salford in Manchester, England.

http://www.soundsfunny.org/ Click on “Ringtones.” The professor is running a survey on which of the sounds is the funniest. Ah, a man after my own heart, collecting and studying rude sounds.

The second photo here shows a self-inflating whoopee cushion that contains a porous Styrofoam and that has a small air vent at the top. After this type is crushed, the Styrofoam tends to expand to its former size, drawing air in through the vent. Within seconds, this type is ready for another acoustic victim.

With either type of whoopee cushion, the rude noises are produced because the air flow through the flat tube is periodic rather than continuous, and the repetition of air bursts causes the tube walls to oscillate. Those walls are formed by two flat rubber sheets that are glued together along their lengths. As you can see in the photos, the tube is narrow at its junction with the inflated part of the cushion and wider at the free end.

As the cushion is crushed under the victim’s weight, the air pressure within the cushion increases until it forces open the tube and pushes air through it. The turbulent onrush of air through the free ends of the flat sheets causes them to flap and to slap together. The rude noises you hear are the sound waves produced by the flapping and slapping.

If the airflow were continuous, the flat sheets would quickly reach some equilibrium position and stop flapping and there would be no noise. However, there is a feedback system that periodically switches between allowing air to flow through the tube and not allowing the flow.

The tube is made so that the two sheets lie flat against each other. When they are forced apart, they must stretch and thus tend to collapse back on each other. They also tend to flex the part near the inflated portion of the cushion so that the opening there closes. For both reasons, once air begins to flow through the tube, the tube collapses, turning off the flow. However, because the cushion is still being crushed by the victim, the air pressure in the cushion again increases until it forces the tube open, and then the cycle is repeated.

An argument can be made that the periodic closing of the tube is due to a reduction of air pressure inside the tube when air flows through it. The argument stems from a rule called the Bernoulli principle, which is a statement about the energy in a moving fluid, here the escaping air. If we can neglect any frictional effects on the fluid from the walls, then the total energy of a fluid must be constant throughout the flow. This means that when the fluid speeds up as it enters a narrow passage, the energy for the increased kinetic energy of the fluid must come from the pressure of the fluid.

In the case of a whoopee cushion, the argument is that as the air moves from the higher pressure region in the cushion and into the narrow escape tube, its pressure decreases. According to the argument, this means that the external atmospheric pressure can then collapse the tube, momentarily turning off the air flow until the cycle is repeated. The argument may be correct, but I don’t see why the reduced pressure in the air flowing through the tube is necessarily lower than the external atmospheric pressure. All I can tell is that it is certainly lower than the high pressure in the cushion.

The frequencies emitted by a whoopee cushion depend on the extent of flapping at the free end and can be roughly controlled by the rate at which the cushion is crushed. A high frequency is produced when the flapping occurs over a short length at the free end. A low frequency (which for various reasons is a far more rude sound) occurs when much of the tube participates in the flapping. Thus, the tube’s length is made long enough to assure that very rude noises are emitted.

Why not vote in his attempt at finding “the funniest whoopee cushion sound”?

Here are links to more web sites:

http://www.youtube.com/watch?v=PVGk85rHjfE video about blowing in a wood instrument or using a whoopee cushion, Professor Trevor Cox. Shows the flapping and slapping of the escape tube in slow motion, and he ends the video with a musical treat produced by several whoopee cushions connected to resonating tubes. It may not be pretty but it beats punk rock.

3.90 Blowing raspberriesJearl Walkerwww.flyingcircusofphysics.comSep 2008 Here is another installment about the physics of rude noises, following my recent story about the physics of whoopee cushions. Blowing raspberries is English slang for a crude, suggestive noise made with the mouth. I find that there are three styles.

1. Tongue style: Stick your tongue out with your lips and teeth closed on the tongue and then blow hard so that the tongue flaps up and down.ttp://www.youtube.com/watch?v=cWGn6_EH2gM high speed video of man blowing raspberries, tongue style

3. Baby style: Press you mouth against the baby with the lips slightly open and then blow hard so that the lips oscillate against the baby. (Babies usually laugh at the rude noise, and so does the parent.)

For all three styles, what makes the noise? They each depend on an oscillation that is set up as air is forced out through a small, flexible opening.

The tongue style might be the easiest to understand. As you build up the air pressure in your mouth, it eventually becomes large enough for the air to force its way between your tongue and the lower teeth and lip, lifting the tongue upward. When the tongue slaps back down on the lower lip, sound is emitted. However, sound is also produced by each pulse of air that escapes — the pulse pushes against the air in front of your mouth, sending a brief pressure wave through the air. The repeated slap and release is the “thbbb thbbb thbbb” that you hear.

In the lip style and the baby style, the lips oscillate and either slap against each other (lip style) or against some other surface (baby style). Again, part of the noise comes from the slapping and part comes from the repeated release of air.

Physics is everywhere, even in rude noises. Well, maybe especially in rude noises.

3.91 Vegetable and fruit musical instrumentsJearl Walkerwww.flyingcircusofphysics.comJan 2010 Here’s the challenge: Pull a fruit or vegetable out of the kitchen and make a musical instrument out of it. There are many examples on the web (links are given below) but here are my two favorites. The first is just right for the Christmas holiday season: “Angels We Have Heard on High” played on broccoli (broccoli!!).

The second is by the well-known Australian musician Linsey Pollak, who shows you how to fashion a clarinet from a carrot and the reed section of a normal clarinet. (Should the construction be called a carrotnet?)

(1) Sound waves are produced when someone blows into or across the instrument. The airflow might pass a thin reed that will oscillate, creating fluctuations in the air pressure (noise). Or the airflow might be onto an edge to create the noise. This might happen if the airflow is across a small opening, as in flute, or into one end, as in a recorder.

(2) Some of the sound waves in the noise set up resonance inside a cavity. Most of the wavelengths of the waves are irrelevant and do not produce audible sound, but some of the wavelengths are just right for setting up resonance. The sound wave with such a wavelength reflects back on itself from the cavity walls (typically at opposite ends) and then reinforces itself instead of canceling itself out. That sound builds in amplitude and becomes audible.

The wavelengths that can be built up like this depend on the length (or general size) of the cavity. A shorter cavity allows only short wavelengths to be built up, which means that frequencies emitted by the instrument are high. Conversely, a longer cavity emits lower frequencies.

In some of the videos, you see a “slide vegetable” (like a slide trombone). When the moveable section slides outward, increasing the length of the cavity, the frequency drops. The effective length of the cavity can also be changed by fingering the holes, to open and close them to control the loss or retention of the internal waves.

(3) Some of the sound built up within the cavity leaks out to be heard. Sound might be transmitted through the cavity walls but usually the sound must escape through an opening, such as at the far end of the instrument from the player or along the sides.

Ok, now your turn. The first video here is an introduction to vegetable instruments. The others are various songs played on a wide variety of instruments, from a cabbage head to an ostrich egg. In each, can you identify the three basic features of the instrument?

3.92 Turning rude and crude noises into musicJearl Walkerwww.flyingcircusofphysics.comSeptember 2010 A schoolboy prank that produces rude sounds has been developed into a musical art form by numerous manualists. You grasp your hands tightly together with an air trapped inside the cavity they form. Then you suddenly squeeze your hands so as to increase the pressure in that trapped air. Some of the air is forced out through a narrow opening between the two hands. The outward flow is not continuous but occurs in bursts because the two sides of the opening oscillate, widening the opening and then collapsing the opening, only to reopen as you continue to increase the air pressure.

And here next is a good example of how the noises have become a form of music. The link takes you to manualist Gerry Philips playing along with Queen on their famous recording “Bohemian Rhapsody.” (If you open up the introductory notes from Philips, you’ll see the message that Brian May sent him about the video. May, who was guitarist and song writer for Queen, finally return to school a few years to complete his Ph.D. in astrophysics. There is my ideal life --- study undergraduate physics, then become a rock and roll star for a few decades, then study graduate physics --- what an ideal life!)

The hand action of a manualist creates sound in two ways: (1) The two sides of the opening periodically slap together. (2) The periodic bursts of air produce a series of pressure waves. The result is that a sound of “thbbb thbbb thbbb” reaches your ears.

The same physics, rudeness, and possible musical career lies beyond a similar rude noise produced with an arm pit. You cup your hand on the arm pit of the opposite arm, trapping air between the hand and the arm pit. Then you bring that arm down quickly to compress the hand and the trapped air. Air periodically bursts out through an oscillating opening between the bottom edge of your hand and the skin over your rib cage. Again, a sound of “thbbb thbbb thbbb” is generated by the periodically slapping of the two sides of the opening and the pressure waves from the periodical bursts of air.

Say, listen. If you are in school and get tired of that math, science, essay writing, and other stuff, then here is a career for you. You can work your way from nightclub to nightclub playing U2 songs on your armpit and arm guitar. Well, maybe not. It would not be the crazy life of a rock and roller. Actually it would be rather sad. Better stick with that math and science, essay writing, and other stuff, and just keep the rude noises at home.

3.93 Pub trick --- popping a plastic strawJearl Walkerwww.flyingcircusofphysics.comDecember 2011 The challenge this month is take a common plastic straw (the wider ones are much better than the narrow cocktail straws) and make it pop loud enough to startle the person sitting next to you in the pub. You might try slapping it against the table, but that is pretty wimpy. A slap is simply not a pop and is unlikely to startle anyone. You might also try slapping the straw directly on the person sitting next to you. That would certainly be startling and would result in a loud pop, but the pop would be from your nose breaking when he hits you in the face.

The solution comes from the delightful book While You’re Waiting for the Food to Come: Experiments and tricks that can be done at a restaurant, the dining room table, or wherever food is served by Eric Muller of The Exploratorium in San Francisco. Pinch the ends of the straw to seal the air inside it. Then, in a “pedaling motion,” twist up the straw, over and over as many times as you can. The straw will fight you as you produce more and more ridges and other curved sections in the plastic, until finally you cannot twist the straw anymore.

Hold the straw horizontally and have a friend flick a finger off the thumb and into the straw, striking the straw sharply with the broad portion of the fingernail. The straw will rupture with a loud pop. Muller advises that the trick may require some practice. Once you and your friend have the technique down, you can certainly draw the attention of the people around you. (Well, they will either be fascinated, which is nice because then you can explain the physics to them. Or they will quickly take their drinks to the other side of the pub, which is nice because then you’ll have more room.)

As explained by Muller, as you twist up the straw, you force the entrapped air into a progressively smaller volume, which causes the pressure in the air to increase. (If you have seen the ideal gas law, you know that the pressure is inversely proportional to the volume because the temperature of the gas is constant. So, as the volume decreases, the pressure increases.)

When the straw is very twisted, the pressure is pretty high and the straw is like an overstressed balloon. However, unlike the balloon, it is fragile. The impact of the fingernail can rupture the straw, allowing the high-pressure air to escape. The sudden outward push by the entrapped air on the surrounding air and the brief flapping of the ruptured plastic send out a sound pulse --- the pop that you hear.

That sudden rupture of the straw is due to two reasons. Although you cannot twist the straw into a smaller volume, the impact of the fingernail can, and the resulting increase in air pressure causes the rupture. Also, the plastic is under a lot of stress due the multiple folds of the plastic. Although the initial, untwisted straw was quite strong against any outward push by the internal air, the folded plastic is not. So, it will rupture at some especially weak point when the fingernail hits.

Reference

Muller, E., While You’re Waiting for the Food to Come: Experiments and tricks that can be done at a restaurant, the dining room table, or wherever food is served, Orchard Books (1999)

3.94 Cell phone camera inside a guitarJearl Walkerwww.flyingcircusofphysics.comMay 2014 Here is a novel idea: slip a small video camera (such as a cell-phone camera) down inside the opening of a guitar so that the camera can record the string through the opening. Then play the strings. Here is an example of the resulting video:

When played, the string oscillates in a superposition (combination) of standing waves. My textbook examines the simplest standing waves separately, not in a superposition. Here is a diagram of how the string oscillates in each of the first three standing waves, said to be the first harmonic (or fundamental), the second harmonic, and the third harmonic.

Each harmonic is produced by waves traveling through each other along the string. In some regions, the waves always cancel. In some regions, they reinforce each other, producing strong displacements of the string. In a textbook or class, we can see how these waves result in the standing waves. Mathematically, we can combine the waves, which are said to be sinusoidal waves because we write either sine functions or cosine functions for them, to produce these simple patterns.

When a guitar string is plucked, several harmonics are set up, depending on where the string is plucked.

If we illuminated the string with a strobe light so that we saw only snapshots (or freeze frames) of the string, we could adjust the strobe frequency to see the standing waves as drawn in a textbook. However, the video camera is not a strobe. Instead, its light sensitive array is exposed in small regions very quickly and then the composite of those exposures appears on the viewing screen. In a normal situation, the composite makes sense but if the camera is recording rapidly moving items at slightly different times, the composite can look strange. Thus, in this video we don’t see the normal sinusoidal waves. Rather we see isolated peaks along a string where the string happened to be displaced when those portions of the scene was recorded. To any physics instructor or musicologist, this video of strange waves instead of sinusoidal waves is unnerving.